Re: proportions

Yes, in a cube and a square which is a face of the same cube, the side length is the same. Use that side length, s, as the "connection". The volume is proportional to : . And the area is proportional to the area: . Eliminate s from those two equations to get a formula in only V and A.

(And what you give: does NOT say "volume is proportional to area", it says "volume cubed is proportional to area squared".)

Re: proportions

Yes. You could also have reasoned that s= A^(1/2) so V= s^3= (A^(1/2))^3= A^(3/2). Notice that here k happens to be 1. It is, in fact, true for any object that the volume is proportional to the surface are to the 3/2 power. For a cube the constant of proportionality is 1.